CASE STUDY SOLUTION
A.
The table or spreadsheet for CSI's unit sales quantity (Q), price (P), optimal advertising
level (A), advertising intensity (A/S), and sales revenue (S) is:
Quantity Price
5,500
$0
5,570
5
5,631
10
5,683
15
5,725
20
5,758
25
5,781
30
5,795
35
5,800
40
5,795
45
5,781
50
5,758
55
5,725
60
5,683
65
5,631
70
5,570
75
5,500
80
5,420
85
5,331
90
5,233
95
5,125
100
Advertising
$25.000
28.125
31.250
34.375
37.500
40.625
43.750
46.875
50.000
53.125
56.250
59.375
62.500
65.625
68.750
71.875
75.000
78.125
81.250
84.375
87.500
Ad/Sales
----10.10%
5.55%
4.03%
3.28%
2.82%
2.52%
2.31%
2.16%
2.04%
1.95%
1.87%
1.82%
1.78%
1.74%
1.72%
1.70%
1.70%
1.69%
1.70%
1.71%
Sales Revenue
$0.00
27,851.56
56,312.50
85,242.19
114,500.00
143,945.31
173,437.50
202,835.94
232,000.00
260,789.06
289,062.50
316,679.69
343,500.00
369,382.81
394,187.50
417,773.44
440,000.00
460,726.56
479,812.50
497,117.19
512,500.00
B.
Based on the CSI table or spreadsheet, the optimal price-advertising combination that
will maximize the number of units sold is the analytical solution P = $40 and A = $5,000.
Notice that quantity rises until this point is reached, but then falls as both price and
advertising climb beyond this point.
C.
The negative quantities and sales revenues observed at very high price-advertising
combinations have a simple analytical interpretation. The quadratic expressions for both
price and advertising are negative in the CSI demand function. At very high levels for
price and advertising, the importance of these negative quadratic terms will outweigh
positive first-order effects. Therefore, at very high levels for price and advertising, both
quantity and sales revenue turn negative. However, negative values for quantity and
sales revenue have no economic interpretation. Remember that price-quantityadvertising relations are clearly sensitive to the price and advertising levels considered.
The nonlinear relation described in the CSI demand function would undoubtedly change
dramatically with dramatic changes in the price-advertising levels considered.